-4+x+7x^2=0

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Solution for -4+x+7x^2=0 equation:


Simplifying
-4 + x + 7x2 = 0

Solving
-4 + x + 7x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
7 the coefficient of the squared term: 

Divide each side by '7'.
-0.5714285714 + 0.1428571429x + x2 = 0

Move the constant term to the right:

Add '0.5714285714' to each side of the equation.
-0.5714285714 + 0.1428571429x + 0.5714285714 + x2 = 0 + 0.5714285714

Reorder the terms:
-0.5714285714 + 0.5714285714 + 0.1428571429x + x2 = 0 + 0.5714285714

Combine like terms: -0.5714285714 + 0.5714285714 = 0.0000000000
0.0000000000 + 0.1428571429x + x2 = 0 + 0.5714285714
0.1428571429x + x2 = 0 + 0.5714285714

Combine like terms: 0 + 0.5714285714 = 0.5714285714
0.1428571429x + x2 = 0.5714285714

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
0.1428571429x + 0.25 + x2 = 0.5714285714 + 0.25

Reorder the terms:
0.25 + 0.1428571429x + x2 = 0.5714285714 + 0.25

Combine like terms: 0.5714285714 + 0.25 = 0.8214285714
0.25 + 0.1428571429x + x2 = 0.8214285714

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 0.8214285714

Calculate the square root of the right side: 0.906326967

Break this problem into two subproblems by setting 
(x + 0.5) equal to 0.906326967 and -0.906326967.

Subproblem 1

x + 0.5 = 0.906326967 Simplifying x + 0.5 = 0.906326967 Reorder the terms: 0.5 + x = 0.906326967 Solving 0.5 + x = 0.906326967 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 0.906326967 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 0.906326967 + -0.5 x = 0.906326967 + -0.5 Combine like terms: 0.906326967 + -0.5 = 0.406326967 x = 0.406326967 Simplifying x = 0.406326967

Subproblem 2

x + 0.5 = -0.906326967 Simplifying x + 0.5 = -0.906326967 Reorder the terms: 0.5 + x = -0.906326967 Solving 0.5 + x = -0.906326967 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -0.906326967 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -0.906326967 + -0.5 x = -0.906326967 + -0.5 Combine like terms: -0.906326967 + -0.5 = -1.406326967 x = -1.406326967 Simplifying x = -1.406326967

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.406326967, -1.406326967}

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